Geometric Sequence Calculator — nth Term, Sum & Infinite Series

A focused geometric sequence and geometric series calculator. Enter the first term a, the common ratio r, and a count n, and read three answers at once: the nth term aₙ = a·r^(n-1), the sum of the first n terms Sₙ = a(1-rⁿ)/(1-r), and the infinite series sum S∞ = a/(1-r) when the ratio converges. The tool lists the actual terms a, ar, ar², ar³, … so you can sanity-check the pattern by eye, and a one-click copy puts the whole sequence on your clipboard. When |r| is 1 or larger, the infinite sum is correctly reported as divergent instead of printing a wrong finite number, and the r = 1 sum falls back to n·a so there is no divide-by-zero. Negative ratios (alternating signs like 3, -6, 12, -24) and fractional ratios (1, ½, ¼, …) are handled. Everything runs locally in the browser with a shareable link that reopens the exact a, r and n.